Wavelet frames on Vilenkin groups and their approximation properties
Classical Analysis and ODEs
2014-12-09 v1 Group Theory
Abstract
An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate Walsh polynomial is described. Approximation properties of tight wavelet frames are also studied. In contrast to the real setting, it appeared that a wavelet tight frame decomposition has an arbitrary large approximation order whenever all wavelet functions are compactly supported.
Cite
@article{arxiv.1412.2699,
title = {Wavelet frames on Vilenkin groups and their approximation properties},
author = {Yuri A. Farkov and Elena A. Lebedeva and Maria A. Skopina},
journal= {arXiv preprint arXiv:1412.2699},
year = {2014}
}
Comments
19 pages